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New contractivity condition in a population model with piecewise constant arguments. (English) Zbl 1161.34048
The author establishes wild class conditions for the contractivity of solutions and the global asymptotic stability for the positive equilibrium of first-order differential equations with piecewise constant arguments. An open problem is also offered and partially answered.

34K25Asymptotic theory of functional-differential equations
34K20Stability theory of functional-differential equations
92D25Population dynamics (general)
Full Text: DOI
[1] Chen, M. P.; Liu, B.: Asymptotic behavior of solutions of first order nonlinear delay difference equations, Comput. math. Appl. 32, 9-13 (1996) · Zbl 0861.39005 · doi:10.1016/0898-1221(96)00119-8
[2] Gopalsamy, K.; Kulenovic, M. R. S.; Ladas, G.: On a logistic equation with piecewise constant arguments, Differential integral equations 4, 215-223 (1991) · Zbl 0727.34061
[3] Gopalsamy, K.; Liu, P.: Persistence and global stability in a population model, J. math. Anal. appl. 224, 59-80 (1998) · Zbl 0912.34040 · doi:10.1006/jmaa.1998.5984
[4] Li, H.; Yuan, R.: An affirmative answer to gopalsamy and Liu’s conjecture in a population model, J. math. Anal. appl. 338, 1152-1168 (2008) · Zbl 1140.34033 · doi:10.1016/j.jmaa.2007.05.081
[5] H. Li, Y. Muroya, R. Yuan, A sufficient condition for the global asymptotic stability of a class of logistic equations with piecewise constant delay. Nonlinear Anal. Real World Appl. (2007), doi:10.1016/j.nonrwa.2007.09.006 · Zbl 1154.34383
[6] Muroya, Y.: Persistence, contractivity and global stability in logistic equations with piecewise constant delays, J. math. Anal. appl. 270, 602-635 (2002) · Zbl 1012.34076 · doi:10.1016/S0022-247X(02)00095-1
[7] Muroya, Y.: Persistence and global stability for discrete models of nonautonomous Lotka -- Volterra type, J. math. Anal. appl. 273, 492-511 (2002) · Zbl 1033.39013 · doi:10.1016/S0022-247X(02)00261-5
[8] Muroya, Y.: A sufficient condition on global stability in a logistic equation with piecewise constant arguments, Hokkaido math. J. 32, 75-83 (2003) · Zbl 1038.34079
[9] Muroya, Y.: Uniform persistence for Lotka -- Volterra type delay differential systems, Nonlinear anal. Real world appl. 4, 689-710 (2003) · Zbl 1044.34035 · doi:10.1016/S1468-1218(02)00072-X
[10] Muroya, Y.: Global stability in discrete models of nonautonomous Lotka -- Volterra type, Hokkaido math. J. 33, 115-126 (2004) · Zbl 1053.39015
[11] Muroya, Y.: Contractivity and global stability for discrete models of Lotka -- Volterra type, Hokkaido math. J. 34, 277-297 (2005) · Zbl 1084.39011
[12] Muroya, Y.: A global stability criterion in scalar delay differential equations, J. math. Anal. appl. 236, 209-227 (2007) · Zbl 1120.34059 · doi:10.1016/j.jmaa.2006.02.074
[13] Muroya, Y.: Global attractivity for discrete models of nonautonomous logistic equations, Comput. math. Appl. 53, 1059-1073 (2007) · Zbl 1151.39007 · doi:10.1016/j.camwa.2006.12.010
[14] Muroya, Y.; Ishiwata, E.; Guglielmi, N.: Global stability for nonlinear difference equations with variable coefficients, J. math. Anal. appl. 334, 232-247 (2007) · Zbl 1126.39007 · doi:10.1016/j.jmaa.2006.12.028
[15] Muroya, Y.; Kato, Y.: On gopalsamy and Liu’s conjecture for global stability for a population model, J. comput. Appl. math. 181, 70-82 (2005) · Zbl 1065.92034 · doi:10.1016/j.cam.2004.11.017
[16] Seifert, G.: Certain systems with piecewise constant feedback controls with a time delay, Differential integral equations 4, 937-947 (1993) · Zbl 0787.93038
[17] So, J. W. -H.; Yu, J. S.: Global stability in a logistic equation with piecewise constant arguments, Hokkaido math. J. 24, 269-286 (1995) · Zbl 0833.34075
[18] Uesugi, K.; Muroya, Y.; Ishiwata, E.: On the global attractivity for a logistic equation with piecewise constant arguments, J. math. Anal. appl. 294, 560-580 (2004) · Zbl 1050.34116 · doi:10.1016/j.jmaa.2004.02.031
[19] Wang, W.; Lu, Z.: Global stability of discrete models of Lotka -- Volterra type, Nonlinear anal. 35, 1019-1030 (1999) · Zbl 0919.92030 · doi:10.1016/S0362-546X(98)00112-6
[20] Wang, W.; Mulone, G.; Salemi, F.; Salone, V.: Global stability of discrete population models with time delays and fluctuating environment, J. math. Anal. appl. 264, 147-169 (2001) · Zbl 1006.92025 · doi:10.1006/jmaa.2001.7666
[21] Yu, J. S.: Asymptotic stability for a linear difference equation with variable delay, Comput. math. Appl. 36, 203-210 (1998) · Zbl 0933.39009 · doi:10.1016/S0898-1221(98)80021-7
[22] Zhou, Z.; Zhang, Q.: Uniform stability of nonlinear difference systems, J. math. Anal. appl. 225, 486-500 (1998) · Zbl 0910.39003 · doi:10.1006/jmaa.1998.6039